Resolution
There is no method to recover the password from the Magelis HMI, however new Security Settings can be downloaded to the HMI.

Option 1:
Modify the security settings in the existing project (or a new project) and download to the HMI via File System to a CF Card or USB Memory Stick media. Then insert the removable media the Magelis HMI to download the application from the CF card.
Steps:
1) In the Vijeo Designer project: change the password or remove it (or create a new empty project)
2) In the Project Navigator, click on the Target node (the name of the HMI)
3) In the Property Inspector, find "Download" and click on the '+' button to expand the node
4) To the right of the word "Download", click the dropdown and select "File System"
5) Plug in an empty CF Card (via an off-the-shelf usb adapter) or USB memory stick (formatted in FAT32) into your computer.
6) Under Download in Vijeo Designer, choose the path "E:\" (or whatever the media shows up as).
7) Right-click on the Target node and select "Download to (File System)" (or go to the Build dropdown menu to download).
8) Once the download is complete, take the removable media out of your PC
9) Insert it into the Magelis HMI. You will be prompted on the HMI to install the project from the USB stick.
10) Touch the button as prompted to proceed.
Result: The new project will be downloaded to the HMI removing or replacing the previous security password settings.

Option 2
Use the Runtime Installer program and run the runtime recovery on the target to bring it to the factory screen.
Steps:
1) Connect a USB cable to the HMI (BMXXCAUSBH018 or XBTZG935) from your configuration PC or connect via Ethernet through a switch/router.
2) From the Start menu of Windows, launch Runtime Installer from "All Programs->Schneider Electric->Vijeo Designer 6.2 -> Tools -> Runtime Installer"
3) Choose either USB or Ethernet as the method of transfer in the first dropdown box
4) If Ethernet was chosen, enter the Ethernet settings to match that of the HMI
5) Click Send and wait for the download to complete
Result: This will download the firmware version of Vijeo Designer that is installed on your PC to the HMI and bring it to the factory screen where the password will be removed for a subsequent download to the HMI.

Note: The above options will not work if "Download Security for USB Media Install" is Enabled in the original project that was downloaded to the HMI. It is Disabled by Default.